Power from mass and acceleration

In summary, the conversation discusses the problem of determining the power required for a 3,219lb car to accelerate at 40.2ft/s^2 and reach 0-60mph in 2.19 seconds. It is mentioned that there is not enough information to accurately calculate this, as the maximum acceleration due to traction limits of the tires is needed. The conversation also delves into the relationship between acceleration, mass, and power, and provides a formula for calculating the required power.
  • #1
LaCalia
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Hello everyone, first post! I'm not terribly fluent in these matters, I'll say to start, but I have a problem.

If a 3,219lb car is capable of accelerating at 40.2ft/s^2, or 0-60mph in 2.19 seconds

How much power must it be capable of producing?

Thanks for your time and patience! :)
 
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  • #2
There's not enough information. What you have is the average acceleration. What's missing is the maximum acceleration possible due to traction limits of the tires.

Technically it takes zero power for the initial acceleration from zero speed. During the period of maximum acceleration, the associated power will increase linearly with speed, since power = force x speed, and force = mass x acceleration.
 
  • #3
Not sure I know what to take away from your answer, but I do wish to clarify that 40.2ft/s^2 is the maximum acceleration do to the bounds of the tires.

I calculated the 0-60 time based on that.
 
  • #4
OK, so maximum acceleration = average acceleration = 40.2 ft / sec^2, due to traction limits. Then the maximum power required is the power required to accelerate a 3,219lb car at 40.2 ft / sec^2 at 60 mph. Note 1 pound mass = 1/32.174 slug (unit of mass). 1 mile = 5280 feet. 1 hour = 3600 seconds. 1 horsepower = 550 ft lb / sec. Force = mass x acceleration.

power = force x speed = ((3219/32.174) x 40.2 ) x (60 x 5280 / 3600) (1/550) ~= 643.5 rwhp (rear wheel horsepower).

It traction allowed for a greater amount of initial acceleration, the required power would be less. The math would be more complicated.
 
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  • #5
Having a little trouble following your maths, but otherwise, I am eternally grateful for your answer!

Thank you!
 
  • #6
I updated my prior post to show what the constants I used in the formula are based on.
 
  • #7
Ah! Well that helps a ton! A million more thanks!
 
  • #8
I won't bother doing the math here, but for a similar problem where the traction is limited at the start (called stage 1 in the post linked below), then acceleration limited by power / speed (called stage 2 in the post linked to below). Given a velocity, total time, maximum acceleration, mass, ..., power could be determined using the formula for velocity (v = ... ) from the post linked to below:

https://www.physicsforums.com/threa...-power-requirement.864834/page-2#post-5443890
 

What is the relationship between mass and acceleration in terms of power?

The relationship between mass and acceleration in terms of power is described by the formula P = m x a, where P is power, m is mass, and a is acceleration. This means that the power produced is directly proportional to both the mass and the acceleration.

How does increasing mass affect the power produced?

Increasing mass will also increase the power produced, as long as the acceleration remains constant. This is because a larger mass requires more force to move, resulting in a higher power output.

What happens to power when both mass and acceleration are increased?

When both mass and acceleration are increased, the power output will increase exponentially. This is because the formula for power (P = m x a) is a multiplication of the two variables, meaning that a small change in either one will have a significant impact on the power produced.

How is power from mass and acceleration utilized in real world applications?

Power from mass and acceleration is utilized in various ways in real world applications. For example, it is used in rocket engines to produce thrust, in cars to generate speed, and in roller coasters to create thrilling rides. It is also used in simple machines such as pulleys and levers to make work easier.

Can power from mass and acceleration be converted into other forms of energy?

Yes, power from mass and acceleration can be converted into other forms of energy. For instance, when a car brakes, the kinetic energy from its motion is converted into heat energy through friction. This concept is also used in regenerative braking systems, where the kinetic energy is converted into electrical energy to recharge the car's battery.

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